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Global goodness-of-fit tests in logistic regression with sparse data
1Institute of Medical Epidemiology, Biostatistics, and Informatics, University of Halle-Wittenberg, 06097 Halle/Saale, Germany. Oliver.Kuss@medizin.uni-halle.de
Statistics in Medicine
|December 17, 2002
Summary
New goodness-of-fit tests for logistic regression models perform better with sparse data than the standard Hosmer-Lemeshow test. These alternative statistical methods offer improved reliability for analyzing medical data with limited observations per covariate pattern.
Area of Science:
- Medical Statistics
- Statistical Modeling
Background:
- Logistic regression is standard for binary responses in medical statistics.
- Assessing goodness-of-fit is challenging, especially with sparse data.
- Standard tests (residual deviance, Pearson chi-square) are unreliable with sparse data.
Purpose of the Study:
- To evaluate alternative goodness-of-fit tests for logistic regression in sparse data scenarios.
- To compare the performance of these alternative tests against the Hosmer-Lemeshow test.
- To identify reliable methods for assessing model fit with limited observations.
Main Methods:
- Simulation study comparing various goodness-of-fit tests.
- Evaluation based on test size and power.
- Application of tests to a real-world dermatology dataset.
Main Results:
- The Hosmer-Lemeshow test exhibits deficiencies and algorithm-dependent results.
- Alternative tests, such as the Farrington test, demonstrate good size and power properties.
- Some alternative tests outperform the Hosmer-Lemeshow test in sparse data conditions.
Conclusions:
- Alternative goodness-of-fit tests offer superior performance for logistic regression with sparse data.
- The Farrington test is a promising alternative for reliable model assessment.
- Careful selection of goodness-of-fit tests is crucial for accurate medical statistical analysis.